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3 years ago

Solve the absolute value equation |x| − 2 = 5 to find the distance Mary can walk forward, x, in 5 seconds.

Mathematics

1 answer:

Alisiya [41]3 years ago

7 0

Answer:

x = 7 m and x = −7 m

Step-by-step explanation:

Its a modulus problem

concept

|x| = x when x>=0

|x| = -x when x < 0

____________________________________

Now given

|x| − 2 = 5

adding 2 both sides

|x| − 2 + 2 = 5 + 2

|x| = 7

now

x = 7 when x >= 0

x = -7 when x<0

Thus, correct answer is x = 7 m and x = −7 m

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Help with this one because I do not know how to do perpendicular plz put explanation with steps worth 50!

Yuri [45]

Answer:

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line $2x-3y=12$ is $3x+2y=34$

Step-by-step explanation:

Given:

$2x-3y=12$

To Find:

Equation of line passing through ( 16, -7) and is perpendicular to the line

$2x-3y=12$

Solution:

$2x-3y=12$ ...........Given

$\therefore y=\dfrac{2}{3}\times x-4$

Comparing with,

$y=mx+c$

Where m =slope

We get

$Slope = m1 = \dfrac{2}{3}$

We know that for Perpendicular lines have product slopes = -1.

$m1\times m2=-1$

Substituting m1 we get m2 as

$\dfrac{2}{3}\times m2=-1\\\\m2=-\dfrac{3}{2}$

Therefore the slope of the required line passing through (16 , -7) will have the slope,

$m2=-\dfrac{3}{2}$

Now the equation of line in slope point form given by

$(y-y_{1})=m(x-x_{1})$

Substituting the point (16 , -7) and slope m2 we will get the required equation of the line,

$(y-(-7))=-\dfrac{3}{2}\times (x-16)\\\\2y+14=-3x+48\\3x+2y=34......Equation\ of\ line$

Therefore, equation of the line that passes through (16,-7) and is perpendicular to the line $2x-3y=12$ is

$3x+2y=34$

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